Nambu-Jona-Lasinio型相互作用下双夸克图像中五夸克态$Θ^+$的Faddeev计算
A Faddeev Calculation for Pentaquark $Θ^+$ in Diquark Picture with Nambu-Jona-Lasinio Type Interaction
摘要：
对Jaffe和Wilczek的双夸克图象中的五夸克态$Θ^+$进行了Bethe-Salpeter-Faddeev（BSF）计算，其中$Θ^+$是一个双夸克-双夸克- ${\bar s}$三体系统.用Nambu-Jona-Lasinio（NJL）模型计算了${\bar s}D$和$D D$两体散射的最低阶图。利用由介子扇区确定的耦合常数，我们发现${\bar s}D$相互作用是吸引的，而$DD$相互作用是排斥的，并且不存在束缚的$\frac 12^+$五夸克态.束缚五夸克态$Θ^+$只有在非物理强的矢量介子耦合常数下才能得到。
英文摘要：
A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $Θ^+$ in the diquark picture of Jaffe and Wilczek in which $Θ^+$ is a diquark-diquark-${\bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${\bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${\bar s}D$ interaction is attractive while $DD$ interaction is repulsive, and there is no bound $\frac 12^+$ pentaquark state. A bound pentaquark $Θ^+$ can only be obtained with unphysically strong vector mesonic coupling constants.
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